1. Doubly Convergent Multiple Beam Guns Lawrence Ives, Thuc Bui, Michael Read Calabazas Creek Research, San Mateo, CA. USA Adam Attarian, Billy Tallis, Cynthia Andujar, Virginia Forstall, Hien Tran N.C. State University, Department of Mathematics, Raleigh, NC 27606 This research was supported by U.S. Department of Energy Grant DE-FG02-06ER86267

2. CCR MBK’s DOE – X-Band 7-beam MBK – 50 MW (cathode failures), 2007 100 kW X-Band (fabricated) –15 beams –perveance 4.5 micropervs (17.6 A @ 25 kV) 150 kW wide band C-Band (in design) –18 beams –Perveance 5.5 micropervs (21.6 A @ 25 kV)

3. Goal Eliminate output power limitation associated with fundamental cavity multiple beam klystrons Beam location in circuit determined by cavity mode Cathodes now required to be at same radius as beam through the circuit Cathode current density limited for long life Limited area for cathodes limits output power

4. Design Tools SolidWorks provides the CAD engine for creation of the parametric geometry Beam Optics Analyzer models electron beam peformance in electrostatic and magnetostatic fields Beam Optics Analyzer GUI controls the process Optimization algorithms evaluate the results and select next configuration Excel provides the transfer of parametric date between optimization algorithms and SolidWorks

5. Goal Function The goal function quantifies the simulation results and compares to required performance Goal function definition is the key to successful results

6. Goal Functions Linearity defines the straightness of the beam at the desired off-axis location

7. Goal Functions Scallop impacts the quality of the beam Other goal functions address beam current, field gradients, magnetic field profile, and collector efficiency.

8. Optimization Procedure for Double Convergence Multiple Beam Gun Goal is to compensate for beam spiraling induced by converging magnetic field Electrons launched with initial azimuthal and radial velocity Linearity optimization adjusts launch angle to obtain linear beam through circuit

9. Scallop Optimization Magnetic field profile is fixed – imported from commercial magnetics code Cathode position in magnetic field profile fixed to provide required beam compression (12:1) Cathode radius of curvature varied to minimize beam scallop

10. Single Beam Geometry Relative positions of cathode, focus electrode, and anode are not modified Grid plates defined perpendicular to device axis at fixed axial locations Beam holes variable to track electron trajectories.

11. Simulation of Single Off-axis Beam Anode, cathode, and focus electrode moved together Two grid plates fixed perpendicular to device axis. Grid holes moved to track beam

12. Final Simulation Results

13. Arrayed Guns

15. Simulation Geometry Not designed for any particular product Magnetic field profile produced from existing solenoid Location of cathode selected for 12:1 area convergence Steepness of convergence greater than would normally be required Design more challenging than for typical product

16. Calculations for 25 MW, 1.0 GHz MBK Assumptions Efficiency 70% (0.45 microP) Beam voltage < 160 kV Max. cathode current density2.8 A/cm 2 No. BeamsVoltage (kV) Current (A) K-diameter (cm) 6 177.3 35.6 3.91 8 158.0 28.3 3.58 10 138.5 25.8 3.42 12 128.8 23.1 3.24

17. Beam Location in Circuit Best performance when beams are close to circuit axis 1.3 GHz MBK beam location in circuit CPI beams 6.0 cm radius from axis Omega-P (Russian design) at 4.6 cm radius Scaled to 1.0 GHz CPI design -> 7.8 cm Omega-P design -> 6.0 cm

18. Scaled CPI Design Single convergent guns can be used 160 kV 25 MW Output

19. Scaled Omega-P Design Insufficient space available for 8 cathodes 160 kV 25 MW Output

20. Scaled CPI Design Single Convergence with 10 beams 140 kV 25 MW Output

21. Double Convergent Guns Allows reduction in beam voltage or increased RF output power by increasing the size or number of electron beams Provides opportunity to place beams closer to the cavity axis for improved performance May impact complexity of gun fabrication - Removes requirement for field-shaping iron near cathodes - Requires careful attention to cathode orientation

22. Schematic Model of 8-Beam MBK 8-Beam MBK 160 kV 25 MW 7:1 Area Compression

23. Questions and Trade-offs Double convergence guns remove existing limitations on output power and beam voltage Mechanical complexity and other issues yet to be determined Is CERN interested in development of double convergent guns? Funding may be available from U.S. Department of Energy if sufficient interested expressed by potential customers. Must justify ~$1M required for the development.